Roots are very powerful. Window screen might slow them down just a bit but if you've ever seen a concrete sidewalk pushed up and broken by tree roots, you can just imagine what they can do to a screen. If you can put down a sheet of metal like a footing around the sides of the bed, and make it a foot or so deep, that should keep out most roots. But in part it depends on what's growing nearby. Some plants/trees are more aggressive than others.

Sandy

I think it would not work to well at all.I think there should be some kind of garden fabric that would be better. Let us know what and how it turns out. GOOD LUCK

Probably not but what are you trying to keep out of your raised bed? Example - Bermuda grass will eventually make its way even through horticultural grade barrier. Also consider the work it will take as well as the disruption to the raised bed, to go back in and fix the problem later. Purchase a good quality horticultural grade weed barrier up front and the jobs done for a long time to come.